In the figure below, all corner angles are right angles and each number represents the unit-length of the segment which is nearest to it. How many square units of area does the figure have?

[asy]

draw((0,0)--(12,0)--(12,5)--(8,5)--(8,4)--(5,4)
--(5,6)--(0,6)--(0,0));

label("6",(0,3),W);
label("5",(2.5,6),N);
label("2",(5,5),W);
label("3",(6.5,4),S);
label("1",(8,4.5),E);
label("4",(10,5),N);

[/asy]
Solution: Partition the figure into rectangles as shown. The area of each rectangle is shown by the circled number in it. Total area $= 30+12+20 = \boxed{62}$.

[asy]

draw((0,0)--(12,0)--(12,5)--(8,5)--(8,4)--(5,4)
--(5,6)--(0,6)--(0,0));

label("6",(0,3),W);
label("5",(2.5,6),N);
label("2",(5,5),W);
label("3",(6.5,4),S);
label("1",(8,4.5),E);
label("4",(10,5),N);

draw((5,0)--(5,4),dashed);
draw((8,0)--(8,4),dashed);
label("4",(5,2),W);
label("4",(8,2),E);

label("30",(2.5,3));
draw(Circle((2.5,3),0.8));

label("12",(6.5,1.5));
draw(Circle((6.5,1.5),0.8));

label("20",(10,2.5));
draw(Circle((10,2.5),0.8));

[/asy]